Concept

Completeness (order theory)

Related lectures (17)

Properties of Real Numbers

Explains the properties of subsets of real numbers, including Supremum, Infimum, intervals, open sets, and closed sets.

From Lattice Products to Tarski's Fixedpoint Theorem

Covers the combination of lattice elements, partial orders, complete lattices, and Tarski's Fixed Point theorem.

Introduction to Real Numbers

Introduces the properties and structure of real numbers, emphasizing completeness and the Archimedean property.

Analytic Structure of Green's Function

Explores the analytic structure of Green's function, bound and scattering states, and perturbation theory.

FSM Design and Synthesis

Explains the design and synthesis of Finite State Machines in logic systems.

Subtyping and Type Calculus

Explores subtyping, type calculus, and type bounds calculation in a system with subtyping, guiding through exercises and proofs step by step.

Properties of Real Numbers: Bounds, Density, Absolute Value

Covers the properties of real numbers, including bounds, density, and absolute value.

Real Numbers: Order and Completeness

Covers the properties of real numbers, focusing on the total order and completeness, including the Archimedean property and the concepts of supremum and infimum.

Linear convergence with Polyak-Łojasiewicz: Strong g-convexity implies PŁ

Explores geodesically strongly convex functions and their relation to the Polyak-Łojasiewicz condition.

Quantum Mechanics and Linear Algebra

Covers Hermitian and Unitary operators, real number equivalents, and eigenvalues.

Introduction to Real Numbers

Introduces the axiomatic structure of real numbers and their properties, including completeness and the Archimedean property.

Petersson Inner Product and Hecke Operators

Covers the Petersson inner product and Hecke operators in modular forms theory, exploring their definitions and properties.

Points Fixes in G-sets

Explores fixed points in G-sets, applications between sets, and the construction of orbits.

Demonstration of Theorem on Compact Functions

Explores the demonstration of a theorem on compact functions and non-regular boundaries.

Completeness of LP

Explores the completeness of LP, discussing implications of mathematical conditions and the convergence of series.

Convergence of Sequences in Multivariable Analysis

Covers the convergence of sequences in multivariable analysis, including definitions, properties, and examples in higher dimensions.

Quantum Computation Delegation

Explores fully classical qubits, blind quantum computing, and verifiability in quantum delegation protocols.